Diffusionless transformation

A diffusionless transformation, commonly known as displacive transformation, denote solid-state alterations in the crystal structure that do not hinge on the diffusion of atoms across extensive distances. Rather, these transformations manifest as a result of synchronized shifts in atomic positions, wherein atoms undergo displacements of distances smaller than the spacing between adjacent atoms, all while preserving their relative arrangement. An exemplar of such a phenomenon is the martensitic transformation, a notable occurrence observed in the context of steel materials. The term "martensite" was originally coined to describe the rigid and finely dispersed constituent that emerges in steels subjected to rapid cooling. Subsequent investigations revealed that materials beyond ferrous alloys, such as non-ferrous alloys and ceramics, can also undergo diffusionless transformations. Consequently, the term "martensite" has evolved to encompass the resultant product arising from such transformations in a more inclusive manner. In the context of diffusionless transformations, a cooperative and homogeneous movement occurs, leading to a modification in the crystal structure during a phase change. These movements are small, usually less than their interatomic distances, and the neighbors of an atom remain close. The systematic movement of large numbers of atoms led to some to refer to these as military transformations in contrast to civilian diffusion-based phase changes, initially by Frederick Charles Frank and John Wyrill Christian.^[1][2]

Diffusionless transformation classifications

The most commonly encountered transformation of this type is the martensitic transformation which, while probably the most studied, is only one subset of non-diffusional transformations. The martensitic transformation in steel represents the most economically significant example of this category of phase transformations. However, an increasing number of alternatives, such as shape memory alloys, are becoming more important as well.

Classification and definitions

When atoms or groups of atoms coordinate to displace their neighboring counterparts resulting in structural modification, this phenomenon is known as a displacive transformation. The scope of displacive transformations is extensive, encompassing a diverse array of structural changes. As a result, additional classifications have been devised to provide a more nuanced understanding of these transformations.^[3]

The first distinction can be drawn between transformations dominated by lattice-distortive strains and those where shuffles are of greater importance.

Homogeneous lattice-distortive strains, also known as Bain strains, transform one Bravais lattice into a different one. This can be represented by a strain matrix S which transforms one vector, y, into a new vector, x:

${\displaystyle y=Sx}$ 

This is homogeneous, as straight lines are transformed into new straight lines. Examples of such transformations include a cubic lattice increasing in size on all three axes (dilation) or shearing into a monoclinic structure.

 

Shuffles, aptly named, refer to the minute displacement of atoms within the unit cell. Notably, pure shuffles typically do not induce a modification in the shape of the unit cell; instead, they predominantly impact its symmetry and overall structural configuration.

Phase transformations typically give rise to the formation of an interface delineating the transformed and parent materials. The energy requisite for establishing this new interface is contingent upon its characteristics, specifically how well the two structures interlock. An additional energy consideration arises when the transformation involves a change in shape. In such instances, if the new phase is constrained by the surrounding material, elastic or plastic deformation may occur, introducing a strain energy term. The interplay between these interfacial and strain energy terms significantly influences the kinetics of the transformation and the morphology of the resulting phase. Notably, in shuffle transformations characterized by minimal distortions, interfacial energies tend to predominate, distinguishing them from lattice-distortive transformations where the impact of strain energy is more pronounced.

A subclassification of lattice-distortive displacements can be made by considering the dilutional and shear components of the distortion. In transformations dominated by the shear component, it is possible to find a line in the new phase that is undistorted from the parent phase while all lines are distorted when the dilation is predominant. Shear-dominated transformations can be further classified according to the magnitude of the strain energies involved compared to the innate vibrations of the atoms in the lattice and hence whether the strain energies have a notable influence on the kinetics of the transformation and the morphology of the resulting phase. If the strain energy is a significant factor, then the transformations are dubbed martensitic, if not the transformation is referred to as quasi-martensitic.

Iron-carbon martensitic transformation

The distinction between austenite and martensite is subtle in nature.^[4] Austenite exhibits a face-centered cubic (FCC) unit cell, whereas the transformation to martensite entails a distortion of this cube into a body-centered tetragonal shape (BCC). This transformation occurs due to a displacive process, where interstitial carbon atoms lack the time to diffuse out.^[5] Consequently, the unit cell undergoes a slight elongation in one dimension and contraction in the other two. Despite marked differences in the mathematical descriptions of these crystal structures owing to symmetry considerations, the chemical bonding between them remains highly similar.

In contrast to cementite, which features bonding akin to ceramic materials, the chemical basis for the hardness of martensite is challenging to elucidate.

The explanation hinges on the crystal's subtle change in dimension. Even a microscopic crystallite is millions of unit cells long. Since all of these units face the same direction, distortions of even a fraction of a percent get magnified into a major mismatch between neighboring materials. The mismatch is sorted out by the creation of crystal defects in work hardening, which results from dislocations within the crystal lattices at the atomic level generated from atomic displacements which serve to prevent the motion of crystal planes under an applied strain. Similar to the process in work-hardened steel, these defects prevent atoms from sliding past one another in an organized fashion, causing the material to become harder.

Shape memory alloys have mechanical properties, which were eventually explained by analogy to martensite. Unlike the iron-carbon system, alloys in the nickel-titanium system can be treated to make the "martensitic" phase thermodynamically stable.

Pseudo martensitic transformation

In addition to displacive transformation and diffusive transformation, a new type of phase transformation that involves a displacive sublattice transition and atomic diffusion was discovered using a high-pressure X-ray diffraction system.^[6] The new transformation mechanism has been christened pseudo martensitic transformation.^[7]

References

Notes

1. D.A. Porter and K.E. Easterling, Phase transformations in metals and alloys, Chapman & Hall, 1992, p.172 ISBN 0-412-45030-5
2. 西山 善次 (1967). "マルテンサイトの格子欠陥" .... 日本金属学会会報 (in Japanese). 6 (7). 日本金属学会: 497–506. doi:10.2320/materia1962.6.497. ISSN 1884-5835. from the original on 2023-06-17 – via J-STAGE.
3. Cohen, Morris; Olson, G. B.; Clapp, P. C. (1979). On the Classification of Displacive Phase Transformations (PDF). International Conference on Martensitic Transformations. pp. 1–11.
4. Duhamel, C.; Venkataraman, S.; Scudino, S.; Eckert, J. (May 2008), "Diffusionless transformations", Basics of Thermodynamics and Phase Transitions in Complex Intermetallics, Book Series on Complex Metallic Alloys, vol. 1, WORLD SCIENTIFIC, pp. 119–145, Bibcode:2008btpt.book..119D, doi:10.1142/9789812790590_0006, ISBN 978-981-279-058-3, retrieved 2023-08-11
5. Shewmon, Paul G. (1969). Transformations in Metals. New York: McGraw-Hill. p. 333. ISBN 978-0-07-056694-1.
6. Chen, Jiuhua; Weidner, Donald J.; Parise, John B.; Vaughan, Michael T.; Raterron, Paul (2001-04-30). "Observation of Cation Reordering during the Olivine-Spinel Transition in Fayalite by In Situ Synchrotron X-Ray Diffraction at High Pressure and Temperature". Physical Review Letters. 86 (18). American Physical Society (APS): 4072–4075. Bibcode:2001PhRvL..86.4072C. doi:10.1103/physrevlett.86.4072. ISSN 0031-9007. PMID 11328098. from the original on 2023-06-17.
7. Leutwyler, Kristin (May 2, 2001). "New Phase Transition May Explain Deep Earthquakes". Scientific American. from the original on 2014-11-17. Retrieved 2023-06-17.

Bibliography

• Christian, J.W., Theory of Transformations in Metals and Alloys, Pergamon Press (1975)
• Khachaturyan, A.G., Theory of Structural Transformations in Solids, Dover Publications, NY (1983)
• Green, D.J.; Hannick, R.; Swain, M.V. (1989). Transformation Toughening of Ceramics. Boca Raton: CRC Press. ISBN 0-8493-6594-5.

External links

• Extensive resources from Cambridge University
• The cubic-to-tetragonal transition
• European Symposium on Martensitic Transformations (ESOMAT)
• PTC Lab for martensite crystallography